Scholarlink

<p>A Hereditarily Indecomposable (HI) Banach space <i>X</i> admits an HI extension if there exists an HI space <i>Z</i> such that <i>X</i> is isomorphic to a subspace <i>Y</i> of <i>Z</i> and <i>Z</i>/<i>Y</i> is of infinite dimension. The problem whether or not every HI space admits an HI extension is attributed to A. Pelczynski. In this paper we present a method to define HI-extensions of the standard HI spaces, a class which includes the Gowers-Maurey space, asymptotic <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell _{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>-HI spaces and others.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The HI extension of the standard HI spaces

  • 期刊论文

  • 发表日期：

    2026年3月28日

查看全文
  • Spiros A. Argyros,
  • Antonis Manoussakis,
  • Pavlos Motakis

摘要

A Hereditarily Indecomposable (HI) Banach space X admits an HI extension if there exists an HI space Z such that X is isomorphic to a subspace Y of Z and Z/Y is of infinite dimension. The problem whether or not every HI space admits an HI extension is attributed to A. Pelczynski. In this paper we present a method to define HI-extensions of the standard HI spaces, a class which includes the Gowers-Maurey space, asymptotic \(\ell _{p}\) ℓ p -HI spaces and others.